// MersenneTwister.h
// Mersenne Twister random number generator -- a C++ class MTRand
// Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
// Richard J. Wagner  v1.1  28 September 2009  wagnerr@umich.edu

// The Mersenne Twister is an algorithm for generating random numbers.  It
// was designed with consideration of the flaws in various other generators.
// The period, 2^19937-1, and the order of equidistribution, 623 dimensions,
// are far greater.  The generator is also fast; it avoids multiplication and
// division, and it benefits from caches and pipelines.  For more information
// see the inventors' web page at
// http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html

// Reference
// M. Matsumoto and T. Nishimura, "Mersenne Twister: A 623-Dimensionally
// Equidistributed Uniform Pseudo-Random Number Generator", ACM Transactions on
// Modeling and Computer Simulation, Vol. 8, No. 1, January 1998, pp 3-30.

// Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
// Copyright (C) 2000 - 2009, Richard J. Wagner
// All rights reserved.
//
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions
// are met:
//
//   1. Redistributions of source code must retain the above copyright
//      notice, this list of conditions and the following disclaimer.
//
//   2. Redistributions in binary form must reproduce the above copyright
//      notice, this list of conditions and the following disclaimer in the
//      documentation and/or other materials provided with the distribution.
//
//   3. The names of its contributors may not be used to endorse or promote
//      products derived from this software without specific prior written
//      permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED.  IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
// POSSIBILITY OF SUCH DAMAGE.

// The original code included the following notice:
//
//     When you use this, send an email to: m-mat@math.sci.hiroshima-u.ac.jp
//     with an appropriate reference to your work.
//
// It would be nice to CC: wagnerr@umich.edu and Cokus@math.washington.edu
// when you write.

#ifndef PIFRO2_MTRAND_H_
#define PIFRO2_MTRAND_H_

// Not thread safe (unless auto-initialization is avoided and each thread has
// its own MTRand object)

#include <iostream>
#include <climits>
#include <cstdio>
#include <ctime>
#include <cmath>

class MTRand {
// Data
public:
  typedef unsigned long uint32;  // unsigned integer type, at least 32 bits

  enum { N = 624 };       // length of state vector
  enum { SAVE = N + 1 };  // length of array for save()

protected:
  enum { M = 397 };  // period parameter

  uint32 state[N];   // internal state
  uint32 *pNext;     // next value to get from state
  int left;          // number of values left before reload needed

// Methods
public:
  MTRand( const uint32 oneSeed );  // initialize with a simple uint32
  MTRand( uint32 *const bigSeed, uint32 const seedLength = N );  // or array
  MTRand();  // auto-initialize with /dev/urandom or time() and clock()
  MTRand( const MTRand& o );  // copy

  // Do NOT use for CRYPTOGRAPHY without securely hashing several returned
  // values together, otherwise the generator state can be learned after
  // reading 624 consecutive values.

  // Access to 32-bit random numbers
  uint32 randInt();                     // integer in [0,2^32-1]
  uint32 randInt( const uint32 n );     // integer in [0,n] for n < 2^32
  //double rand();                        // real number in [0,1] -- disabled by rtoso
  //double rand( const double n );        // real number in [0,n] -- disabled by rtoso
  double randExc();                     // real number in [0,1)
  double randExc( const double n );     // real number in [0,n)
  double randDblExc();                  // real number in (0,1)
  double randDblExc( const double n );  // real number in (0,n)
  double operator()();                  // same as rand53()

  // Access to 53-bit random numbers (capacity of IEEE double precision)
  double rand();    // calls rand53() -- modified by rtoso
  double rand53();    // real number in [0,1)

  // Access to nonuniform random number distributions
  double randNorm( const double mean = 0.0, const double stddev = 1.0 );

  // Re-seeding functions with same behavior as initializers
  void seed( const uint32 oneSeed );
  void seed( uint32 *const bigSeed, const uint32 seedLength = N );
  void seed();

  // Saving and loading generator state
  void save( uint32* saveArray ) const;  // to array of size SAVE
  void load( uint32 *const loadArray );  // from such array
  friend std::ostream& operator<<( std::ostream& os, const MTRand& mtrand );
  friend std::istream& operator>>( std::istream& is, MTRand& mtrand );
  MTRand& operator=( const MTRand& o );

protected:
  void initialize( const uint32 oneSeed );
  void reload();
  uint32 hiBit( const uint32 u ) const {
    return u & 0x80000000UL;
  }
  uint32 loBit( const uint32 u ) const {
    return u & 0x00000001UL;
  }
  uint32 loBits( const uint32 u ) const {
    return u & 0x7fffffffUL;
  }
  uint32 mixBits( const uint32 u, const uint32 v ) const
  {
    return hiBit(u) | loBits(v);
  }
  uint32 magic( const uint32 u ) const
  {
    return loBit(u) ? 0x9908b0dfUL : 0x0UL;
  }
  uint32 twist( const uint32 m, const uint32 s0, const uint32 s1 ) const
  {
    return m ^ (mixBits(s0,s1)>>1) ^ magic(s1);
  }
  static uint32 hash( time_t t, clock_t c );
};

// Functions are defined in order of usage to assist inlining

inline MTRand::uint32 MTRand::hash( time_t t, clock_t c )
{
  // Get a uint32 from t and c
  // Better than uint32(x) in case x is floating point in [0,1]
  // Based on code by Lawrence Kirby (fred@genesis.demon.co.uk)

  static uint32 differ = 0;  // guarantee time-based seeds will change

  uint32 h1 = 0;
  unsigned char *p = (unsigned char *) &t;
  for( size_t i = 0; i < sizeof(t); ++i )
  {
    h1 *= UCHAR_MAX + 2U;
    h1 += p[i];
  }
  uint32 h2 = 0;
  p = (unsigned char *) &c;
  for( size_t j = 0; j < sizeof(c); ++j )
  {
    h2 *= UCHAR_MAX + 2U;
    h2 += p[j];
  }
  return ( h1 + differ++ ) ^ h2;
}

inline void MTRand::initialize( const uint32 seed )
{
  // Initialize generator state with seed
  // See Knuth TAOCP Vol 2, 3rd Ed, p.106 for multiplier.
  // In previous versions, most significant bits (MSBs) of the seed affect
  // only MSBs of the state array.  Modified 9 Jan 2002 by Makoto Matsumoto.
  register uint32 *s = state;
  register uint32 *r = state;
  register int i = 1;
  *s++ = seed & 0xffffffffUL;
  for( ; i < N; ++i )
  {
    *s++ = ( 1812433253UL * ( *r ^ (*r >> 30) ) + i ) & 0xffffffffUL;
    r++;
  }
}

inline void MTRand::reload()
{
  // Generate N new values in state
  // Made clearer and faster by Matthew Bellew (matthew.bellew@home.com)
  static const int MmN = int(M) - int(N);  // in case enums are unsigned
  register uint32 *p = state;
  register int i;
  for( i = N - M; i--; ++p )
    *p = twist( p[M], p[0], p[1] );
  for( i = M; --i; ++p )
    *p = twist( p[MmN], p[0], p[1] );
  *p = twist( p[MmN], p[0], state[0] );

  left = N, pNext = state;
}

inline void MTRand::seed( const uint32 oneSeed )
{
  // Seed the generator with a simple uint32
  initialize(oneSeed);
  reload();
}

inline void MTRand::seed( uint32 *const bigSeed, const uint32 seedLength )
{
  // Seed the generator with an array of uint32's
  // There are 2^19937-1 possible initial states.  This function allows
  // all of those to be accessed by providing at least 19937 bits (with a
  // default seed length of N = 624 uint32's).  Any bits above the lower 32
  // in each element are discarded.
  // Just call seed() if you want to get array from /dev/urandom
  initialize(19650218UL);
  register int i = 1;
  register uint32 j = 0;
  register int k = ( N > seedLength ? N : seedLength );
  for( ; k; --k )
  {
    state[i] =
      state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1664525UL );
    state[i] += ( bigSeed[j] & 0xffffffffUL ) + j;
    state[i] &= 0xffffffffUL;
    ++i;
    ++j;
    if( i >= N ) {
      state[0] = state[N-1];
      i = 1;
    }
    if( j >= seedLength ) j = 0;
  }
  for( k = N - 1; k; --k )
  {
    state[i] =
      state[i] ^ ( (state[i-1] ^ (state[i-1] >> 30)) * 1566083941UL );
    state[i] -= i;
    state[i] &= 0xffffffffUL;
    ++i;
    if( i >= N ) {
      state[0] = state[N-1];
      i = 1;
    }
  }
  state[0] = 0x80000000UL;  // MSB is 1, assuring non-zero initial array
  reload();
}

inline void MTRand::seed()
{
  // Seed the generator with an array from /dev/urandom if available
  // Otherwise use a hash of time() and clock() values

  // First try getting an array from /dev/urandom
  FILE* urandom = fopen( "/dev/urandom", "rb" );
  if( urandom )
  {
    uint32 bigSeed[N];
    register uint32 *s = bigSeed;
    register int i = N;
    register bool success = true;
    while( success && i-- )
      success = fread( s++, sizeof(uint32), 1, urandom );
    fclose(urandom);
    if( success ) {
      seed( bigSeed, N );
      return;
    }
  }

  // Was not successful, so use time() and clock() instead
  seed( hash( time(NULL), clock() ) );
}

inline MTRand::MTRand( const uint32 oneSeed )
{
  seed(oneSeed);
}

inline MTRand::MTRand( uint32 *const bigSeed, const uint32 seedLength )
{
  seed(bigSeed,seedLength);
}

inline MTRand::MTRand()
{
  seed();
}

inline MTRand::MTRand( const MTRand& o )
{
  register const uint32 *t = o.state;
  register uint32 *s = state;
  register int i = N;
  for( ; i--; *s++ = *t++ ) {}
  left = o.left;
  pNext = &state[N-left];
}

inline MTRand::uint32 MTRand::randInt()
{
  // Pull a 32-bit integer from the generator state
  // Every other access function simply transforms the numbers extracted here

  if( left == 0 ) reload();
  --left;

  register uint32 s1;
  s1 = *pNext++;
  s1 ^= (s1 >> 11);
  s1 ^= (s1 <<  7) & 0x9d2c5680UL;
  s1 ^= (s1 << 15) & 0xefc60000UL;
  return ( s1 ^ (s1 >> 18) );
}

inline MTRand::uint32 MTRand::randInt( const uint32 n )
{
  // Find which bits are used in n
  // Optimized by Magnus Jonsson (magnus@smartelectronix.com)
  uint32 used = n;
  used |= used >> 1;
  used |= used >> 2;
  used |= used >> 4;
  used |= used >> 8;
  used |= used >> 16;

  // Draw numbers until one is found in [0,n]
  uint32 i;
  do
    i = randInt() & used;  // toss unused bits to shorten search
  while( i > n );
  return i;
}

//inline double MTRand::rand()
//  { return double(randInt()) * (1.0/4294967295.0); }

//inline double MTRand::rand( const double n )
//  { return rand() * n; }

inline double MTRand::randExc()
{
  return double(randInt()) * (1.0/4294967296.0);
}

inline double MTRand::randExc( const double n )
{
  return randExc() * n;
}

inline double MTRand::randDblExc()
{
  return ( double(randInt()) + 0.5 ) * (1.0/4294967296.0);
}

inline double MTRand::randDblExc( const double n )
{
  return randDblExc() * n;
}

inline double MTRand::rand53()
{
  uint32 a = randInt() >> 5, b = randInt() >> 6;
  return ( a * 67108864.0 + b ) * (1.0/9007199254740992.0);  // by Isaku Wada
}

inline double MTRand::rand()
{
  return rand53();
}

inline double MTRand::randNorm( const double mean, const double stddev )
{
  // Return a real number from a normal (Gaussian) distribution with given
  // mean and standard deviation by polar form of Box-Muller transformation
  double x, y, r;
  do
  {
    x = 2.0 * rand53() - 1.0;
    y = 2.0 * rand53() - 1.0;
    r = x * x + y * y;
  }
  while ( r >= 1.0 || r == 0.0 );
  double s = sqrt( -2.0 * log(r) / r );
  return mean + x * s * stddev;
}

inline double MTRand::operator()()
{
  return rand53();
}

inline void MTRand::save( uint32* saveArray ) const
{
  register const uint32 *s = state;
  register uint32 *sa = saveArray;
  register int i = N;
  for( ; i--; *sa++ = *s++ ) {}
  *sa = left;
}

inline void MTRand::load( uint32 *const loadArray )
{
  register uint32 *s = state;
  register uint32 *la = loadArray;
  register int i = N;
  for( ; i--; *s++ = *la++ ) {}
  left = *la;
  pNext = &state[N-left];
}

inline std::ostream& operator<<( std::ostream& os, const MTRand& mtrand )
{
  register const MTRand::uint32 *s = mtrand.state;
  register int i = mtrand.N;
  for( ; i--; os << *s++ << "\t" ) {}
  return os << mtrand.left;
}

inline std::istream& operator>>( std::istream& is, MTRand& mtrand )
{
  register MTRand::uint32 *s = mtrand.state;
  register int i = mtrand.N;
  for( ; i--; is >> *s++ ) {}
  is >> mtrand.left;
  mtrand.pNext = &mtrand.state[mtrand.N-mtrand.left];
  return is;
}

inline MTRand& MTRand::operator=( const MTRand& o )
{
  if( this == &o ) return (*this);
  register const uint32 *t = o.state;
  register uint32 *s = state;
  register int i = N;
  for( ; i--; *s++ = *t++ ) {}
  left = o.left;
  pNext = &state[N-left];
  return (*this);
}

#endif  // PIFRO2_MTRAND_H_

// Change log:
//
// v0.1 - First release on 15 May 2000
//      - Based on code by Makoto Matsumoto, Takuji Nishimura, and Shawn Cokus
//      - Translated from C to C++
//      - Made completely ANSI compliant
//      - Designed convenient interface for initialization, seeding, and
//        obtaining numbers in default or user-defined ranges
//      - Added automatic seeding from /dev/urandom or time() and clock()
//      - Provided functions for saving and loading generator state
//
// v0.2 - Fixed bug which reloaded generator one step too late
//
// v0.3 - Switched to clearer, faster reload() code from Matthew Bellew
//
// v0.4 - Removed trailing newline in saved generator format to be consistent
//        with output format of built-in types
//
// v0.5 - Improved portability by replacing static const int's with enum's and
//        clarifying return values in seed(); suggested by Eric Heimburg
//      - Removed MAXINT constant; use 0xffffffffUL instead
//
// v0.6 - Eliminated seed overflow when uint32 is larger than 32 bits
//      - Changed integer [0,n] generator to give better uniformity
//
// v0.7 - Fixed operator precedence ambiguity in reload()
//      - Added access for real numbers in (0,1) and (0,n)
//
// v0.8 - Included time.h header to properly support time_t and clock_t
//
// v1.0 - Revised seeding to match 26 Jan 2002 update of Nishimura and Matsumoto
//      - Allowed for seeding with arrays of any length
//      - Added access for real numbers in [0,1) with 53-bit resolution
//      - Added access for real numbers from normal (Gaussian) distributions
//      - Increased overall speed by optimizing twist()
//      - Doubled speed of integer [0,n] generation
//      - Fixed out-of-range number generation on 64-bit machines
//      - Improved portability by substituting literal constants for long enum's
//      - Changed license from GNU LGPL to BSD
//
// v1.1 - Corrected parameter label in randNorm from "variance" to "stddev"
//      - Changed randNorm algorithm from basic to polar form for efficiency
//      - Updated includes from deprecated <xxxx.h> to standard <cxxxx> forms
//      - Cleaned declarations and definitions to please Intel compiler
//      - Revised twist() operator to work on ones'-complement machines
//      - Fixed reload() function to work when N and M are unsigned
//      - Added copy constructor and copy operator from Salvador Espana
